sculpt tools act in incorrect direction
Since sculpting tools usually act based on the normals of vertices (e.g: an additive inflate brush will push verts forwards along their normals, and a subtractive one will push them the other way), there are a couple causes for this. The most common of which are:

Inverted normals: If the vertex normals are inversed, sculpting will act in the opposite of the expected direction.  Solution: Go into edit mode, select everything, Ctrl+N or Alt+N to recalculate normals or flip them from the specials menu (W)
Negative scale: Scale will cause the vertex normals to be reversed - thus have the same effect as mentioned above.  Solution: Apply the scale in object mode (Ctrl+A), or reset it (Alt+S)
Non-uniform scale: This won't cause the sculpt direction to be inverted, but it will cause strange and often unpredictable issues such as a narrower/wider than expected brush radius.  Solution: Same as above.

As with any issue in Blender, the two first things you should check are whether the normal directions are correct and the object scale is uniform and positive.
Also see: Why is it important to apply transformation